{"as_of":"2026-08-11T01:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fbed484f982d71286cd4ef8e4a62a4314f5def1400e0f387873cacbd37159158","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T04:45:42.340068Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-13T02:41:32.458647Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.08583","snapshot_observed_at":"2026-07-13T02:41:32.458647Z","title":"The density of elliptic curves overQp with a rational 3-torsion point or a rational 3-isogeny.arXiv preprint arXiv:2502.08583, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09483","last_updated":"2026-07-10T15:00:06Z","snapshot_observed_at":"2026-08-05T04:57:13.783781Z","submitted_at":"2026-07-10T15:00:06Z","title":"Counting odd genus $2$ curves with a marked rational $3$-torsion point","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-13T02:41:32.458647Z"},"links":{"cited_paper":"/paper/2502.08583","citing_paper":"/paper/2607.09483"},"observation_digest":"sha256:1fdbb0dde826769fd67105335453104f9726f5fb001acd4bfacd3a3273b39ba1","observation_id":"c68e1e8d-c62c-4939-afe8-6c81fd5641a1","resolution":{"observed_at":"2026-07-13T02:41:32.458647Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2502.08583/citation-record","integrity":"/paper/2502.08583/integrity","json":"/paper/2502.08583/citation-record.json","paper":"/paper/2502.08583"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.325007Z","title":"Jacobians of genus one curves","venue":null,"work_id":"ca54baaa-ec62-4872-b8ec-62ee898f0240","year":2001},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.064689Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:fc95c1786fc0274873c54f7c6dfc72e622864e79f022b29be29ffd2101aacb5f","observation_id":"df3626fa-806e-4857-a8ec-49f4bbeb1f71","resolution":{"observed_at":"2026-08-08T04:45:43.328310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.314398Z","title":"The Hesse pencil of plane cubic curves","venue":null,"work_id":"78bc2a90-1059-4fc9-82f0-3ead6acfd106","year":2009},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.088982Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:0e09f1fe7b658558b6a981083385bb73bfb07a3685963e2ca43bd3cdf79065d4","observation_id":"9e8e5e97-bbc7-417d-9f39-a0474437d0c4","resolution":{"observed_at":"2026-08-08T04:45:43.317816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.00891","last_updated":"2025-05-12T20:04:26Z","snapshot_observed_at":"2026-08-09T07:33:27.876520Z","submitted_at":"2024-09-02T02:00:12Z","title":"Shadow line distributions","version":2},"cited_work":{"arxiv_id":"2409.00891","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.00891","snapshot_observed_at":"2026-08-08T04:45:42.504302Z","title":"Shadow line distributions","venue":"math.NT","work_id":"456ad703-cedd-4b44-af7f-ee2791a35d52","year":2024},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.105912Z"},"links":{"cited_paper":"/paper/2409.00891","citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:ff5fcabb1f974e4f33b1e747ab63f1b756b6e0a023603f6658d1ba810c7c85c1","observation_id":"ec6c3ac6-44aa-4bbd-a728-b52f275a81ab","resolution":{"observed_at":"2026-08-08T04:45:42.508092Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.06584","last_updated":"2024-05-10T16:39:35Z","snapshot_observed_at":"2026-07-06T18:12:43.301678Z","submitted_at":"2024-05-10T16:39:35Z","title":"How often does a cubic hypersurface have a rational point?","version":1},"cited_work":{"arxiv_id":"2405.06584","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.06584","snapshot_observed_at":"2026-08-08T04:45:42.487875Z","title":"How often does a cubic hypersurface have a rational point?","venue":"math.NT","work_id":"c6459f1d-ca42-4bbc-ac1f-4223f08b4c95","year":2024},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.133550Z"},"links":{"cited_paper":"/paper/2405.06584","citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:b1e84953fb414bc893de834527fc96a7017278c8baa9012378c4b972c47df746","observation_id":"8266ab7c-ab47-42b6-a819-537561c8618a","resolution":{"observed_at":"2026-08-08T04:45:42.492285Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.303583Z","title":"Higher composition laws IV: The parametrizat ion of quintic rings","venue":null,"work_id":"ede5c98e-f920-4025-85e7-17866f262ba5","year":2008},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.137401Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:82628add982ae859cfc38799c76abfee0b5578b36f31d4cd45304523eee03cdd","observation_id":"6bee02ef-7163-4377-9d1b-a6f1f26748d2","resolution":{"observed_at":"2026-08-08T04:45:43.307194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.292879Z","title":"The proport ion of plane cubic curves over Q that everywhere locally have a point","venue":null,"work_id":"68ee66b9-c93c-4a7e-b0b8-5191267d7bcb","year":2016},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.141104Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:a2a544be15f6ceceb27ef16ee5a02977e8d585b01ec9339bf716b4274a5976dd","observation_id":"a6a6b0ae-d2ea-4ea4-94c6-0a9b44ea424c","resolution":{"observed_at":"2026-08-08T04:45:43.296300Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.281526Z","title":"The proport ion of genus one curves over Q defined by a binary quartic that everywhere locally have a point","venue":null,"work_id":"d080a773-8bf2-45d7-8b9a-bb5a4934d9ef","year":2021},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.144479Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:4b85dd5d041938aad72e8665951e60071d16c781f9067cd8846b4acbd9aa2ecb","observation_id":"5d380947-c18c-41b4-83ab-1e8047e1b6fa","resolution":{"observed_at":"2026-08-08T04:45:43.285377Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.243809Z","title":"The density of polynomials of degree n over Zp having exactly r roots in Qp","venue":null,"work_id":"21041c46-6e43-421c-949b-f5ecfecc781c","year":2022},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.147259Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:bfc8b9a658bcc45233235db41b2b3d9743aeb3c46dd9d708ae7d81056f4b9ba1","observation_id":"ddf50e42-74bc-4b3a-8db9-900c793dba5e","resolution":{"observed_at":"2026-08-08T04:45:43.273571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.176367Z","title":"The Magma alg ebra system","venue":null,"work_id":"a3208c49-6996-49b2-a6d0-4a679567a25d","year":1997},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.149885Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:abb357e460d19e11a5302cedc95dd0beb8b165e592612eecd685d10806ecac49","observation_id":"217fe8e3-ab6c-442d-9f16-1bcb39bbf2a5","resolution":{"observed_at":"2026-08-08T04:45:43.184785Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:43.011101Z","title":"Counting elliptic curves with prescrib ed level structures over number fields","venue":null,"work_id":"a7d5ba81-f4a9-49dc-bcd6-68df32a2bed3","year":2022},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.153620Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:8c7d40bf4a96aa7e5b609a2e962687dfa19ae3e23bf2fe72eed644e00adea613","observation_id":"4a96f09f-bbeb-4632-81d6-3cd7be222dc6","resolution":{"observed_at":"2026-08-08T04:45:43.132245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.915583Z","title":"Local and global densities for Weierstrass models of elliptic curves","venue":null,"work_id":"1c04ddfc-62db-4744-955d-59ad29ae2bf2","year":2023},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.156315Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:c21f3db52b1091e0ea746257f1478da71b96557c1267dd6cccbf6df5dc179c4d","observation_id":"322ae437-5b24-467a-8457-b2c5e05e21d7","resolution":{"observed_at":"2026-08-08T04:45:42.919949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.904119Z","title":"On a probabilistic local-global principle for torsion on elliptic curves","venue":null,"work_id":"a9b06095-c5be-4e29-b7ac-0d1e7c563b00","year":2022},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.159728Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:221cdaa901a30af604d267baf56516571b46cafa656b0233448e036094df7dd0","observation_id":"131e69cf-b211-4e93-9639-9a24e0fbdd0b","resolution":{"observed_at":"2026-08-08T04:45:42.908214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.893054Z","title":"Report on Igusa’s local zeta function","venue":null,"work_id":"cf549013-ea26-4aa6-87c0-202f6fe6bf36","year":1990},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.162704Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:e3a7ce1ee367a22e38ce76e80e57a0adfa89cfdb47ca2607184187b4098dc290","observation_id":"ec32e6fd-3581-402f-bff6-9fac45fb9045","resolution":{"observed_at":"2026-08-08T04:45:42.896835Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.882033Z","title":"Die Typen der Multiplikatorenringe elliptischer Funkt ionenk¨ orper","venue":null,"work_id":"ece7c490-50a2-42ff-89f6-c05078df3133","year":1941},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.166047Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:7f154e13c983c5637b9c504e3bf7d76f8525fc88317ea5e7c7657cbf8a944977","observation_id":"e0ef0d45-0c60-471a-9205-bc6b5fab2f45","resolution":{"observed_at":"2026-08-08T04:45:42.885932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.870296Z","title":"The invariants of a genus one curve","venue":null,"work_id":"d9f83166-293b-4b50-a426-dfa01a9100a5","year":2008},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.168738Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:28c662639a50d7afe69f3a81a4d7127cc0e9052c54a00e57a3b9c05506a70e98","observation_id":"05b2283b-e44e-4426-ae0c-20badf9072cb","resolution":{"observed_at":"2026-08-08T04:45:42.873905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.859523Z","title":"The hessian of a genus one curve","venue":null,"work_id":"dcca3404-dc9f-4268-a0cd-4c42d31a0a50","year":2012},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.171588Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:63da2e281dd7bc23be330492ae6dec9acd39848315339fa7cc7b917ee6147437","observation_id":"5d487495-586a-4175-bd06-9b5d146fc9b5","resolution":{"observed_at":"2026-08-08T04:45:42.862965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.848240Z","title":"A formula for the Jacobian of a genus one curve of a rbitrary degree","venue":null,"work_id":"1f95f62d-247a-40a7-bc0a-f2cf0f97b902","year":2018},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.175039Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:f60c92f7d61fcb30a406eff15f9e5e45e191f9283010df95d5c24f276c24add3","observation_id":"2f791ddd-cdcf-4e00-a0e9-d3a85232a769","resolution":{"observed_at":"2026-08-08T04:45:42.852399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.835743Z","title":"Everywhere local solub ility for hypersurfaces in products of projective spaces","venue":null,"work_id":"531d6a3c-d383-40e1-8577-98ee3f0dfe3d","year":2021},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.178329Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:68aaaebe564f927effc3a54bbaef1f503d81bc9eb5c07335bef7295c77d42f16","observation_id":"606209a8-215a-4425-ab69-37939228efc6","resolution":{"observed_at":"2026-08-08T04:45:42.839803Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.820615Z","title":"Counting elliptic curves wit h prescribed torsion","venue":null,"work_id":"4bb31481-62b2-47e9-b518-4302e4bf58a7","year":2017},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.181537Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:d2eb05691659edff325b06a50a83ab186a074808701ca4fd0706a20b770897da","observation_id":"43daffe4-2372-4427-80f0-7f66653c5b73","resolution":{"observed_at":"2026-08-08T04:45:42.826685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.184772Z","title":"Algebraic geometry, volume 52","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.184772Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:ed0f90e9594ba4f237bd41b998f0b67dffce4ee1642c4942414e10626bee9904","observation_id":"6554bb26-1d61-4ad9-a265-c76f8f078412","resolution":{"observed_at":"2026-08-08T04:45:42.184772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.795200Z","title":"An introduction to the theory of local zeta functions , volume 14","venue":null,"work_id":"7e9dda56-c050-49b5-9745-24fcd5a8f1c0","year":2000},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.187756Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:272027b426d20e7c950c770c9f78789b72f06d28b37a832376d4e242fbad37e0","observation_id":"a869c94a-55da-4487-8873-609701fc1a51","resolution":{"observed_at":"2026-08-08T04:45:42.802604Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.190548Z","title":"Algebraic geometry and arithmetic curves , volume 6","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.190548Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:8241e00c8b85bad097203ba424ae543792535bc9fb44b83acf0d9dffb25be794","observation_id":"ae873990-9ddf-4aee-a47b-1b787a487eb3","resolution":{"observed_at":"2026-08-08T04:45:42.190548Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.775998Z","title":"Elliptic cur ves and formal groups","venue":null,"work_id":"1f59c817-064e-4fd8-b33b-d64b8f14d4e5","year":1964},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.193857Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:d69efcad9b0f3bf292a54f831e4754e23be5e47db59d8df63d547e07c4b70dad","observation_id":"f04bfd45-995f-4334-969a-a04c159eb226","resolution":{"observed_at":"2026-08-08T04:45:42.779513Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.763724Z","title":"Multiplicative functions inshort intervals","venue":null,"work_id":"44704a7d-0bc8-439e-9a0a-aa123bc9e7d1","year":2016},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.197485Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:2881aab975d3c1204046e037f737cdff8f3d9c34384025c3e51fef2dd650f853","observation_id":"85aa2d24-e96e-4197-b2f1-944fffd32288","resolution":{"observed_at":"2026-08-08T04:45:42.767976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.654005Z","title":"A note on elliptic curves with ordinary reduct ion","venue":null,"work_id":"90d13b98-1458-4c7a-aa80-e87149a75f87","year":1993},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.200969Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:6388ba3d3a0f41f8c5a61a9a5c6aacac48f70611696e97e97260dfac8f96c1a9","observation_id":"c9565e07-7dfc-4e48-b7c6-e4b1146a40b8","resolution":{"observed_at":"2026-08-08T04:45:42.690767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1211.5833","last_updated":"2013-01-30T16:43:47Z","snapshot_observed_at":"2026-07-06T03:00:36.393810Z","submitted_at":"2012-11-26T01:26:06Z","title":"On p-torsion of p-adic elliptic curves with additive reduction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1211.5833","snapshot_observed_at":"2026-08-08T04:45:42.204496Z","title":"On p-torsion of p-adic elliptic curves with additive reduction","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.204496Z"},"links":{"cited_paper":"/paper/1211.5833","citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:2c40955464d69309d69e0182fc5da3ad911998afde4eb2b0074085491a98721a","observation_id":"fbb1bde7-ecf2-408b-ad41-a95030a5ec58","resolution":{"observed_at":"2026-08-08T04:45:42.204496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.597590Z","title":"Counting elliptic curves with an isogeny of degree three","venue":null,"work_id":"ba08e79f-20c0-4b32-9a47-3c2021babb15","year":2020},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.207970Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:67fc4770e090775b3d4b05e49c0c3f65f28e2bbe658a3e1366e30fd6ee8b10fb","observation_id":"cd4be2d4-b92d-4187-b870-bb19cc9cadfb","resolution":{"observed_at":"2026-08-08T04:45:42.620333Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.575480Z","title":"Families of elliptic curves with constant modp representations","venue":null,"work_id":"5990f040-58fa-4549-99c8-c1904ec662e4","year":1995},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.211755Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:3ba1d791fbd5af28325f8be456dc73f0f89b5b534d2f030ebb78e1519c87652c","observation_id":"b8fc3c8c-44ad-40ac-840c-f28739f361ea","resolution":{"observed_at":"2026-08-08T04:45:42.579328Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.563494Z","title":"Une formule de masse pour les extensions t otalement ramifiees de degres donne d’un corps local","venue":null,"work_id":"ecfad6e9-e9c3-4276-b454-b61ff3941023","year":1978},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.215208Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:69bf58e7f4ff91fcfb8841331dfb2f6519cf6184565f047f8b89d2eace401efa","observation_id":"90bce357-929a-484d-ae03-a3804fb8a81b","resolution":{"observed_at":"2026-08-08T04:45:42.567264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1904.13063","last_updated":"2019-04-30T06:03:04Z","snapshot_observed_at":"2026-08-09T07:34:38.211097Z","submitted_at":"2019-04-30T06:03:04Z","title":"Families of elliptic curves ordered by conductor","version":1},"cited_work":{"arxiv_id":"1904.13063","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.13063","snapshot_observed_at":"2026-08-08T04:45:42.439508Z","title":"Families of elliptic curves ordered by conductor","venue":"math.NT","work_id":"3f6704fb-a1d1-42fe-b09b-6d2684f62d2b","year":2019},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.219071Z"},"links":{"cited_paper":"/paper/1904.13063","citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:fe2526f77b60ea216d00ac3be0e5d412575573f58c05b19338e3fedd75d29d42","observation_id":"1d06ca20-6807-4ee2-87ba-7bc6e25d9f26","resolution":{"observed_at":"2026-08-08T04:45:42.461576Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.550808Z","title":"The arithmetic of elliptic curves , volume 106","venue":null,"work_id":"9b65f94d-edbe-431a-aad7-8ba4cc3149bb","year":2009},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.223337Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:708f6be657c95748659df7751cbe1e68ec5685020e43d54d1b2d357eb005eaae","observation_id":"5adf635a-69bf-4202-b040-6fa170c9e6be","resolution":{"observed_at":"2026-08-08T04:45:42.554806Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.539023Z","title":"The discrete logarithm problem on elliptic curves of trace one","venue":null,"work_id":"269a6c36-c30a-4b59-9e9e-487f5c4bd5f0","year":1999},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.244830Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:1d734605a5d52cc200a539b5478a0e45ec419022687aa18ce8b81094950d2ce1","observation_id":"482c0822-9e4a-4b64-b25d-8d681499565f","resolution":{"observed_at":"2026-08-08T04:45:42.543162Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.527113Z","title":"Algorithm for determining the type of a singular fiber in an elliptic pencil","venue":null,"work_id":"ce935759-5bd7-4d61-99c2-e74a4768b652","year":1972},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.284168Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:6b40afe3eae330c7ca06aa3011720539acd02405bb9fb77a7f2470b5c8565a6f","observation_id":"c2fe6b1e-f6dc-4f07-8bf2-41d87119f6d7","resolution":{"observed_at":"2026-08-08T04:45:42.531219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T04:45:42.515649Z","title":"The greatest common valuatio n of φn and ψ2 n at points on elliptic curves","venue":null,"work_id":"25a2110f-8930-4d76-b20c-db92d96de8ee","year":2021},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.307463Z"},"links":{"citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:065ed804192088466a281b389d20a0aae51fbac9ef1a9e72fd7587410184a5c9","observation_id":"6ea61844-7674-4be9-9fa3-d59bf1190741","resolution":{"observed_at":"2026-08-08T04:45:42.519252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.10688","last_updated":"2024-09-18T16:43:06Z","snapshot_observed_at":"2026-08-09T07:34:52.330201Z","submitted_at":"2024-09-16T19:35:28Z","title":"Local solubility of a family of ternary conics over a biprojective base I","version":2},"cited_work":{"arxiv_id":"2409.10688","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.10688","snapshot_observed_at":"2026-08-08T04:45:42.394194Z","title":"Local solubility of a family of ternary conics over a biprojective base I","venue":"math.NT","work_id":"c5af5b98-2215-4562-bf91-3092f9d03b4e","year":2024},"citing_paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-08T04:45:42.340068Z"},"links":{"cited_paper":"/paper/2409.10688","citing_paper":"/paper/2502.08583"},"observation_digest":"sha256:8b96e60a8525a84f73b8c81168642f5bdaac2b9d4328cb0ca2c22cde1ecc1d8b","observation_id":"1c155c96-4460-4ef7-91e2-2b353fddbf16","resolution":{"observed_at":"2026-08-08T04:45:42.410438Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2502.08583","last_updated":"2025-04-18T21:13:47Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-09T07:33:51.298334Z","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":4,"verified_fuzzy":28},"total_outbound_references":35},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2502.08583."}